Stochastic Modelling of Reaction–Diffusion Processes

Practical introduction for advanced undergraduate or beginning graduate students of applied mathematics, developed at the University of Oxford.

Radek Erban (Author), S. Jonathan Chapman (Author)

9781108703000, Cambridge University Press

Paperback / softback, published 30 January 2020

319 pages, 8 b/w illus. 86 colour illus. 3 tables 88 exercises
22.8 x 15.2 x 1.3 cm, 0.45 kg

'This book is also available at a reduced price as an e-book on Kindle. Based on the sample I viewed, all the features of the printed book have been perfectly preserved, with no loss of clarity in the layout or the mathematical symbols or the graphs and diagrams.' David Hopkins, The Mathematical Gazette

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

1. Stochastic simulation of chemical reactions
2. Deterministic versus stochastic modelling
3. Stochastic differential equations
4. Diffusion
5. Efficient stochastic modelling of chemical reactions
6. Stochastic reaction-diffusion models
7. SSAs for reaction-diffusion-advection processes
8. Microscopic models of Brownian motion
9. Multiscale and multi-resolution methods
Appendix A. Deterministic modelling of chemical reactions
Appendix B. Discrete probability distributions
Appendix C. Continuous probability distributions
References
Index.

Subject Areas: Mathematical modelling [PBWH], Probability & statistics [PBT]